Related papers: Flipped Quartification and a composite $b$-quark
A new type of algebras that represent a generalization of both quantum groups and braided groups is defined. These algebras are given by a pair of solutions of the Yang--Baxter equation that satisfy some additional conditions. Several…
The edge-to-edge tilings of the sphere by congruent quadrilaterals of Type $a^2bc$ are classified as $3$ classes: a sequence of two-parameter families of $2$-layer earth map tilings with $2n$ $(n\ge3)$ tiles, a one-parameter family of…
We derive a partial electric-magnetic (PEM) duality transformation of the twisted quantum double (TQD) model TQD$(G,\alpha)$---discrete Dijkgraaf-Witten model---with a finite gauge group $G$, which has an Abelian normal subgroup $N$, and a…
We construct a large class of multipartite qudit states which are positive under the family of partial transpositions. The construction is based on certain direct sum decomposition of the total Hilbert space displaying characteristic…
We explain the orthogonal planes split (OPS) of quaternions based on the arbitrary choice of one or two linearly independent pure unit quaternions $f,g$. Next we systematically generalize the quaternionic Fourier transform (QFT) applied to…
We provide a quantum model for the recent experiment coupling a tardigrade to superconducting qubits. A number of different perspectives are discussed with the emphasis placed on quantum entanglement between different subsystems involved in…
A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.
There are three quarks with masses at or below the characteristic scale of QCD dynamics: up, down and strange. However, twisted mass lattice QCD relies on quark doublets. Various options for including three quark flavors within the twisted…
We introduce a modified version of the necklace Lie bialgebra associated to a quiver, in which the bracket and cobracket insert (rather than remove) pairs of arrows in involution. This structure is then related to canonical quartic…
With a q-deformed quantum mechanical framework, features of the uncertainty relation and a novel formulation of the Schr\"odinger equation are considered.
The aim of the paper is to provide an method to obtain representations of the braid group through a set of quasitriangular Hopf algebras. In particular, these algebras may be derived from group algebras of cyclic groups with additional…
We use the $q$-characters to compute explicit expressions of the $R$-matrices for first fundamental representations of all types of twisted quantum affine algebras.
In this paper we present an approach to quadratic structures in derived algebraic geometry. We define derived n-shifted quadratic complexes, over derived affine stacks and over general derived stacks, and give several examples of those. We…
The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this note, I discuss some aspects of this more general Fourier…
We discuss the concept of how entanglement changes with respect to different factorizations of the total algebra which describes the quantum states. Depending on the considered factorization a quantum state appears either entangled or…
The formulation of the alternative theory of neutrino oscillations is presented. Also the application of that theory to a system of neutrinos produced by a source is formulated and some basic formulae are derived.
We construct the quartic version of generalized quasi-topological gravity, which was recently constructed to cubic order in arXiv: 1703.01631. This class of theories includes Lovelock gravity and a known form of quartic quasi-topological…
There are eight quarks in each family and there are three families of quarks i.e. c, b, t. Also, we propose similar structure for leptons. The nature of strong force is named as `third order electroweak'.
We propose a quantum cloning machine, which clones a qubit into two clones assuming known modulus of expectation value of Pauli Z-matrix. The process is referred to as the mirror phase-covariant cloning, for which the input state is a…
A recent parameterisation scheme developed for the quark mixing matrix is shown to be easily applicable to the lepton mixing matrix as well.